ABSTRACT
A reasonable approach to developing numerically reliable algorithms for computational problems in linear system theory would be to reformulate the problems as concatenations of subproblems for which numerically stable algorithms are available. Unfortunately, one cannot ensure that the stability of algorithms for the subproblems results in the stability of the overall algorithm. This requires separate analysis that may rely on the sensitivity or condition of the subproblems. In the next section, we show that delicate (i.e., badly conditioned) subproblems should be avoided whenever possible; a few examples are given where a possibly badly conditioned step is circumvented by carefully modifying or completing existing algorithms; see, for example, [14, p. 109].
